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Math Help - matrix algebra

  1. #1
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    matrix algebra

    v1 = [1,-3,2] v2 = [-3,9,-6] v3 = [5,-7,h]. For what values of h is v3 in the Span(v1, v2}? For what values of h is {v1,v2,v3} linearly independent?

    When I row reduce the matrix, I get 1 -3 5 0
    0 0 8 0
    0 0 h-10 0

    So for when h = 10 the v3 is in the span of v1 and v2?
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  2. #2
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    Quote Originally Posted by lord12 View Post
    v1 = [1,-3,2] v2 = [-3,9,-6] v3 = [5,-7,h]. For what values of h is v3 in the Span(v1, v2}? For what values of h is {v1,v2,v3} linearly independent?

    When I row reduce the matrix, I get 1 -3 5 0
    0 0 8 0
    0 0 h-10 0

    So for when h = 10 the v3 is in the span of v1 and v2?
    Did you notice that Span\{v_1, v_2\} = Span\{v_1\} = Span\{v_2\}? You can use this fact (once you've identified why it's a fact, of course) to answer both questions without even approaching a matrix.
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